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Association for Symbolic Logic, Journal of Symbolic Logic, 01(65), p. 259-271

DOI: 10.2307/2586535

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Filters, Cohen Sets and Consistent Extensions of the Erdos-Dushnik-Miller Theorem

Journal article published in 2000 by Saharon Shelah, Lee J. Stanley
This paper is available in a repository.
This paper is available in a repository.

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Abstract

We present two different types of models where, for certain singular cardinals $λ$ of uncountable cofinality, $λ → (λ,ω + 1)^2$, although $λ$ is not a strong limit cardinal. We announce, here, and will present in a subsequent paper, [7], that, for example, consistently, $ℵ_{ω_1} ↛ (ℵ_{ω_1}, ω + 1)^2$ and consistently, 2$^{ℵ_0} ↛ (2^{ℵ_0},ω + 1)^2$.